Basic Geometric Constructions

Back to Triangles

The simplest geometric construction is the duplication of a given length.

Step 1: To duplicate the length of a given straight line segment AB, put the compass point on point A and open it to point B.

Step 2: Draw a straight line L of convenient length. Mark point A near one end. Without changing the compass setting, put the compass point on point A and mark point B.

The exact length of the given line segment AB has been transferred to line L.

The next construction is to draw the perpendicular bisector of a given line segment. This is simply a line which is perpendicular to segment AB and passes through it's midpoint.
Step 1: Put the compass point on point A and open it to more than half the length of segment AB. Draw an arc through the segment as shown.
Step 2: Without changing the compass setting, draw a second arc by putting the compass point on point B. The two arcs will intersect at two points as shown.
Step 3: Draw line XY through the two points where the arcs intersect. This is the perpendicular bisector of segment AB.
The next construction has to do with angles. Given an arbitrary angle, draw a line which divides (bisects) the angle into two equal angles.
Step 1: Open the compass to a convenient length. Put the compass point on point A and draw an arc through the given angle.
Step 2: Put the compass point on point B and draw an arc as shown.
Step 3: Without changing the compass setting, put the compass point on point C and draw another arc as shown.
Step 4: Draw a straight line XY through point A and the point where the two arcs intersect. This is the angle bisector.